Dynamics Response of Beam on Elastic Foundation with Axial Force to Partially Distributed Moving Loads

Abstract

The dynamics response of Beam on elastic foundation with axial force to partially distributed moving loads was examined. The fourth order  partial differential equation which is the governing equation  was first reduced to second order differential equation by assume a solution in form of series solution and maple software was finally employed to obtain numerical solution in order to determine the behaviour of the system of discussion. The effect of mass of the beam on both the moving force and the moving mass were examined. It was noted that increase in mass of the beam is an increase in the transverse displacement for both the moving force and the moving mass with respect to both the tensile and the compressive forces. Again, it was observed that as the axial force increases, the displacement decreases under the action of the moving force but reverse is the case for the moving mass in that, as the axial force increases the displacement is equally increases for the tensile force but for compressive force, the displacement increases as the axial force increases. More so, it was discovered that deflection due to compressive force is greater than that due to tensile force. Furthermore, it was discovered that the displacement decreases as the elastic foundation (k) increases for both the moving force and the moving mass for fixed value of M and S with respect to tensile force and compressive force. Finally, the deflection due to compressive force is greater than that due to tensile force while the deflection due to moving mass is greater than that due to moving force.